Unexpected Teapots...

Sometime in 1952, Bertrand Russell launched a teapot into orbit around the sun somewhere between the Earth and Mars, and then promptly lost track of the vessel [1]. While Russell’s Teapot was, sadly, entirely hypothetical; invented as an example of an untestable assertion so he could make an argument about the burden of proof, it also raises another question of critical importance to a world populated by more than seven billion people, and their many billions more electronic devices, with an ever growing demand for electrical power;

How long would it take to boil a pot of tea in orbit around the sun, between Earth and Mars?

There is nothing inherently magical about electricity; you can’t conjure it with an incantation or an elaborate hand gesture, it has to come from somewhere. Since you’re here on Electrical Fun, it’s fairly safe to assume you already know this, but it bears repeating. Batteries produce electricity via chemical reaction, and solar cells absorb photons and convert their energy into current. Internal combustion engines generate mechanical power by exploding small quantities of combustible gas hundreds or thousands of times per minute, pushing one or more pistons in sequence to rotate a driveshaft. If you attach a magnet to the other end of that shaft, and allow it to spin inside a coil of conductive wire, you’ve built an electrical generator.

As it turns out though, a significant fraction of the electricity pushed onto the electrical grid which eventually powers our TVs and toasters and charges our phones, is in fact generated by teapots.

Somewhere in space between Earth and Mars, Russell’s Teapot is spinning quite rapidly, even though the water within has boiled off long ago, because that water, converted into pressurized steam by a combination of continuous direct solar radiation and rapid low-pressure evaporation, turned the spout into a jet nozzle for a few brief moments. For the first few minutes, after the steam cloud rapidly cooled and froze, the Teapot would have been surrounded by a twinkling spiral cloud of ice crystals, looking very much like a tiny model galaxy, but that cloud has long since dissipated, the ice crystals carried off by their own momentum and the same radiative pressure that creates comets’ tails, leaving Russell’s Teapot dizzy and alone in the vast empty night.

You can imagine my disappointment when, years ago, after watching hundreds of hours of Star Trek, Star Wars, Babylon 5 and too many other SF series and films to count, I discovered that nuclear power was generated by steam engines. Steam engines! I grew up literally down the street from a coal-burning power plant, reading books by Bradbury and Asimov, imagining spaceships powered by immense glowing engines that hummed with the energy they tore out of the very fabric of reality itself, and then it turned out that ‘nuclear power’ only meant that uranium, when allowed to undergo radioactive decay in very controlled conditions, produces enough heat to boil water and produce steam which turns turbines in exactly the same way as the coal-burning plant at the end of my street.

... a very complicated teapot. source: Wikimedia

Sometime in the sixty-five years since Russell launched his teapot into solar orbit, and it set itself pinwheeling through space like an off-balance steam rocket, it has passed through many diffuse clouds of rocky debris left over from the formation of the solar system. Here on Earth, when our planet passes through these clouds, some of which are so large and so ancient that we’ve given them names; Perseid, Leonid, Orionid, and so on. We can predict the appearance of these meteor showers with remarkable precision [2]. The shooting stars we see on a clear night are bits of rock falling through the Earth’s atmosphere, heated by tremendous friction until they vaporize, glowing and burning briefly across the night sky. Some of these are quite large, perhaps the size of cars before they are torn apart in the sky, but those are relatively rare. Most meteors are roughly gravel sized, and never even make it to the ground.

But Russell’s Teapot doesn’t have an atmosphere, unless you count the handful of ice crystals it’s managed to hang onto with its infinitesimal gravitational field, and there is nothing to stop a pea-sized meteor from striking it with the full force of their combined orbital energy. If Russell had launched a metal tea kettle instead, it might be largely intact, perhaps with a handful of new holes punched through its thin skin. Russell favored china teapots though, which means even a single impact likely shattered our lonely satellite decades ago.

Perhaps not, though. Both of the Voyager probes, launched in 1977, have been traveling through the Solar System at high velocity ever since. Both probes passed through the asteroid belt between Mars and Jupiter intact, and both probes continue to operate, albeit at reduced power levels, today, having passed into the heliosheath almost a decade or more ago. Granted, satellites and probes are engineered to be more robust than a teapot, but at 1800 pounds each, both Voyagers are about the size of a small car, and present a much larger target. Perhaps Russell’s Teapot has similarly avoided a deadly collision. The Solar System is, after all, very very big, and almost entirely empty.

Voyager 1 is now the most distant man-made object in existence, reporting back at nearly 138 astronomical units (AU). One AU is roughly the distance between the Earth and the Sun, or about 93 million miles. Light travels from the Sun to the Earth in about eight minutes, but a radio signal between Earth and Voyager 1, traveling at the speed of light, requires over eighteen hours to reach its destination, and Voyager 1 has been traveling through space for 39 years.

Space is really, really big, and there are no convenience stores along the way to stop off for fresh batteries. So how is Voyager 1 still sending and receiving messages after all this time when your cellphone barely lasts eight hours on a single charge? The answer to that question is once again nuclear power, but in this case there’s no teapot involved; the Voyagers are powered by radioisotope thermoelectric generators; basically a lead bottle containing a quantity of radioactive material to produce heat as it decays, a heat sink, and between the two a thermocouple to convert the temperature gradient into a slow, steady electrical current over the lifetime of the probe. Between its three RTGs, Voyager 1 produced 470 watts at the time of its launch which sounds impressive, but keep in mind that four decades later the power output has fallen to 315 watts [3], and an electric tea kettle uses 1500 watts to boil a single cup of water in under two minutes. If you were to use a Voyager probe to make an entire pot of tea, you’d have to wait twenty minutes or more for it to boil, but you wouldn’t have to worry about cleaning up the dishes while they safely traveled away from your kitchen sink at thirty-eight thousand miles per hour.

But now that we’ve been around the sun a few times and to the edge of the heliosphere, let’s return to Russell’s Teapot, still in orbit, miraculously intact, somewhere between Earth and Mars, and answer that question I asked at the start of this essay. How long would it take to boil a pot of water here? We’ve already discussed the rapid boiling that occurs in space due to the lack of atmospheric pressure, and I’m going to now ignore it completely; tea isn’t tea if it isn’t boiled at 212°F (or 100°C, if your tea is metric), and the kind of boiling that occurs when water is exposed to a vacuum happens at temperatures far lower than that. Even if you don’t mind cold tea, it is kind of difficult to enjoy biscuits and tiny sandwiches while drinking a cloud of tea-flavored ice crystals, so let’s switch things up a bit, and use Russell’s Teapot as a solar collector to power an electric kettle inside our spacecraft, where we have convenient artificial gravity, and exactly one atmosphere of pressure.

Feel free to correct my math here, preferably in lengthy, periphrastic letters written on as many twenty dollar bills as you require to get your point across.

Tea is serious business. source: puretea.com

A teapot is essentially a sphere ten centimeters in diameter; I know this, because I googled it, and the kind of people who both own teapots and have an inclination toward measuring them use the metric system for everything except for volumes of beer and the typical distance between their source of beer and the table where they plan to drink it. That teapot would have a cross section of about seventy-eight and a half square centimeters, which is not a neat, round number, so let’s assume Russell is really fond of tea, and owns a teapot approximately eleven and a third centimeters in diameter, so we can deal with a cross section of exactly one hundred square centimeters.

Back to Google again; mean Solar irradiance at Earth orbit is 1361 W/m², and at Mars the figure is less than half that; 586 W/m² [4]. Assuming Russell’s Teapot operates at nearly 100% efficiency as a solar cell (which is impossible), we will only need to wait several hours for our tea to boil, or deploy a few hundred more teapots to prepare our tea in any reasonable amount of time.

/This is clearly a terrible idea/, but you knew that when I suggested it. The real reason I’ve taken you on this odd tour of the solar system and introduced a number of methods of power generation was simply to get you here, in orbit around the Earth, thinking about solar power. At any given moment, the total electrical consumption of all the devices on Earth is about twenty terawatts. We already know that the Sun throws a bit more than a kilowatt at every square meter of space on the imaginary sphere that surrounds it at the distance of the Earth’s orbit; solar panels on Earth lose about a third of that energy to atmospheric scattering, and commercial panels have increased in efficiency from 14% to as high as 17% at present [5], so ground-based solar farms collect roughly 135 watts per square meter; less in the morning and evening, and none at night. Cutting to the chase here, in order to power the world with exclusively solar, we would need to build solar farms with a total area of six-hundred billion square meters.

Graph of solar radiation reaching the Earth’s surface over a 24-hour period. Peaking ~900W/m². Drops in radiation are generally due to passing clouds.
source: NOAA Global Radiation Group

For scale, Texas is roughly seven-hundred billion square meters in area [6]. Sacrificing Texas for this project is unlikely to end well for anybody involved, and even if this weren’t the largest land-based civil engineering project ever proposed, transmission losses over thousands of miles of power lines makes the idea of one centralized solar farm infeasible and ridiculous. Before we start crunching number to see how large a solar array would need to be for the average city, town, and village, let’s remember where we are; /in space/.

In space, beyond the Earth’s atmosphere that stole a third of the power from us. In space, where night happens only briefly when our satellites pass through the Earth’s shadow at high velocity once per orbit, and then only if its orbit is in the same plane as the Earth’s orbit around the sun. If we put our satellite into an orbit inclined a few degrees above or below the ecliptic, we can guarantee that it spends 99% or more of its time in direct sunlight [7]. Instead of an effective 35W/m² for ground-based solar farms, a solar array in orbit should achieve closer to 200W/m², requiring a total area of only one-hundred billion square meters; a little bit smaller than Kentucky. That array would have to be larger to include redundancy for malfunctions and collision damage, and larger still to make up for the inevitable losses incurred when the collected power is converted into microwaves for transmission back to Earth, but that’s a small problem compared to the major problem with this idea:

/How do we get all of those satellites up there, anyhow?/

I’m glad you’ve asked. Would you care to take a trip to the Moon? Grab your 3D printer and follow me...